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MATH / Let P(x) be a quadratic polynomial with real coefficients satisfying x²−2x+2≤P(x)≤2x²−4x+3 for all real numbers x, and suppose P(11)=181. Find P(16).

Problem

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problem

Let P(x)P(x) be a quadratic polynomial with real coefficients satisfying x2−2x+2≤P(x)≤2x2−4x+3x^2 - 2x + 2 \le P(x) \le 2x^2 - 4x + 3 for all real numbers xx, and suppose P(11)=181P(11) = 181. Find P(16)P(16).
Plain-text mathematical notation (without MathML)
Let P(x) be a quadratic polynomial with real coefficients satisfying x²−2x+2≤P(x)≤2x²−4x+3 for all real  numbers x, and suppose P(11)=181. Find P(16).
Original LaTeX notation
Let $P(x)$ be a quadratic polynomial with real coefficients satisfying $x^2 - 2x + 2 \le P(x) \le 2x^2 - 4x + 3$ for all real  numbers $x$, and suppose $P(11) = 181$. Find $P(16)$.

level

Level 4

type

Intermediate Algebra

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Source and history

task_id
7ee46247-9618-54a7-8f2f-822fec382219
task_key
intermediate~5falgebra--test--7ee46247-9618-54a7-8f2f-822fec382219
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import